Total sight deposits held by the SNB increased to 751.28 billion francs from 749.61 billion francs a week earlier, according to bank data.
The rise followed a 2.5 billion franc increase a week earlier.
An increase can indicate the SNB is active in the currency markets, buying foreign currencies from commercial banks in exchange for newly created francs, thereby increasing their sight deposit accounts.
Analysts said the increase could represent a small return to the market to slow the recent appreciation of the Swiss franc, which has risen to 0.9646 francs to the euro, its highest level since January 2015.
The SNB has said it is prepared to tolerate a stronger franc, which keeps a brake on Swiss inflation by keeping import prices down, but it will also act if the currency became too weak or too strong.
The central bank declined to comment on Monday.
"Looking at this weeks and last week's rise in sight deposits there is indeed the possibility of interventions to slow the rise in the Swiss franc," said UBS economist Alessandro Bee.
"However, I don't think that the SNB is ready to put a floor on EURCHF at this level, which would imply massive interventions," added Bee, who said stronger interventions were an option if the exchange rate went to 0.95 francs to the euro.
Maxime Botteron, an economist at Credit Suisse, said it was currently difficult to determine the SNB's actions due to it providing liquidity to commercial banks through repurchase agreements (repos).
"Any FX purchases remain unlikely with the current level of inflation. As long as inflation remains elevated, I see very little chance for the SNB to buy foreign currencies," Botteron said.
($1 = 0.9463 Swiss francs)
(Reporting by John Revill; Editing by Alison Williams)